Problem: $J$ is the midpoint of $\overline{CT}$ $C$ $J$ $T$ If: $ CJ = 6x - 2$ and $ JT = 8x - 16$ Find $CT$.
Answer: A midpoint divides a segment into two segments with equal lengths. ${CJ} = {JT}$ Substitute in the expressions that were given for each length: $ {6x - 2} = {8x - 16}$ Solve for $x$ $ -2x = -14$ $ x = 7$ Substitute $7$ for $x$ in the expressions that were given for $CJ$ and $JT$ $ CJ = 6({7}) - 2$ $ JT = 8({7}) - 16$ $ CJ = 42 - 2$ $ JT = 56 - 16$ $ CJ = 40$ $ JT = 40$ To find the length $CT$ , add the lengths ${CJ}$ and ${JT}$ $ CT = {CJ} + {JT}$ $ CT = {40} + {40}$ $ CT = 80$